Question

Three dentists wanted to compare the ages of their patients. They each calculated their patients’ mean age and the mean absolute deviation of their ages. They displayed the results in a table.
Which statements are true?

Select each correct answer.

Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.

Dr. Singh’s patients’ ages and Dr. Appiah’s patients’ ages vary about the same amount.

Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.

Dr. Appiah’s patients’ ages vary more than do Dr. Cantwell’s patients’ ages.
Dentist Mean patient age MAD
Appiah 43 9.7
Cantwell 29 13.9
Singh 41 14.1

Answer 1

Its Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages and Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.

Answer 2

Answer:

As, Mean is defined as sum of all observations divided by total number of observations.

And, Mean absolute Deviation is defined as Sum of absolute differences of each data from mean divided by total number of observation.

The greater the Mean absolute deviation ,greater the dispersion.

As, mean of all the three patients are different , as well as mean absolute deviation.

Option 1: Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.

As, you can also say that Option 3 , can be also true, which is Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount because there is little bit of difference in Mean absolute deviation of Dentist Cantwell and Singh.

But, only Option 1: is completely true.